natural frequency of a hanging tube with two guided supports

[nanoman40]

a hanging aluminum 6061 tube (from a long 3/16 aircraft cable). Dimensions: 3.125" OD x .125" wall x 120" long. ~20 lb distributed. guide support at bottom and guide support at 90 inches from bottom (30 inches from top). How to calculate the natural frequency? Any help would be appreciated.

Thank you in advance.

 

[MikeyP]

The book "Formulas for natural frequency and modeshape" by RD Blevins should have the answer.

M

--
Dr Michael F Platten

 

[volvibeguy]

Have you any connections or a friend with a Vibration Analyser, if so you may try bump/impact testing to obtain information about the natural as well as excited frequencies.

 

[vanstoja]

There may be as many as four types of vibrations involved, two of which require the length, modululus of elasticity and area of the supporting cable. First is the extensional mode of the concentrated bar mass at the end of the cable
f=(1/2pi)*(k/M)^0.5 where k=EA/L for the cable. Second is the pendulum mode (between the guide boundaries)of the concentrated mass about the cable end pivot point f=(1/2pi)*g/L where L is cable length. Third is the beam bending modes of the rod with end and 2/3*l guided or hinged supports where l is tube length. Tables 8-3a to f in Blevins give equations and parametric data for 6 modes of up to 15 equal spans of pinned supports. Table 12-1 in Blevins gives equations for shell modes of the tube in the unrestrained condition, at best an apprtoximation to a guided tube's shell responses. The total range of "natural frequencies" for these four types of vibration probably range from very low (pendular<10 Hz) to rather high (shell modes>1000 Hz)so criticality of calculation accuracies depends on what kind of damage concerns you.

 

[magnograil]

Must be heavy aluminum, I get about 14.1 lbs. Not clear on what natural frequency you are looking for. Vertical vibration of mass on the end of an elastic cable spring? Bending of tube? Which direction is the guide support restraining? Acoustic or mechanical resonance?